It is hypothesized that the blue-green color of the eggshells of many avian species represents an informational signal as to the health of the female that laid the eggs. To investigate this hypothesis, researchers conducted a study in which birds assigned to the treatment group were provided with supplementary food before and during laying; they predict that if eggshell coloration is related to female health at laying, females given supplementary food will lay more intensely blue-green eggs than control females. Nests were paired according to when nest construction began, and the study examined 16 nest pairs.

(a) The blue-green chroma (BGC) of eggs was measured on the day of laying; BGC refers to the proportion of total reflectance that is in the blue-green region of the spectrum, with a higher value representing a deeper blue-green color. In the food supplemented group, BGC chroma had \(\bar{x}=0.594\) and \(s=0.010\); in the control group, BGC chroma had \(\bar{x}=0.586\) and \(s=0.009\). A paired \(t\)-test resulted in \(t=2.28\) and \(p=0.038\). Interpret the results in the context of the data.

(b) In general, healthier birds are also known to lay heavier eggs. Egg mass was also measured for both groups. In the food supplemented group, egg mass had \(\bar{x}=1.70\) grams and \(s=0.11\) grams; in the control group, egg mass had \(\bar{x}=0.586\) grams and \(s=0.009\) grams. The test statistic from a paired \(t\)-test was 2.64 with \(p\)-value 0.019 . Compute and interpret a \(95 \%\) confidence interval for \(\delta\), the population mean difference in egg mass between the groups.